Interferometry measurement is a technique to measure the distance to a target or targets using wavelengths such as light. It can be used in many different fields and applications including: long distance measurement, 3-dimensional positioning where the ability to measure simultaneously to multiple targets from a single interferometer is particularly advantageous (using mainly frequency only) and small displacements (using also phase) for engineering and aerospace applications; surface inspection and imaging for quality control devices; short range detailed imaging for biological applications like the optical coherence tomography (OCT) techniques.
Frequency Scanning Interferometry (FSI, also known as Frequency Sweeping Interferometry) is one type of interferometry that is used to measure the distance to a cooperative, reflecting target or a non-cooperative, specular surface using light. It is also known as Wavelength Shifting Interferometry, Frequency Modulated Continuous Wave ranging and laser radar. An example implementation is shown in FIG. 1.
FSI uses an interferometer to illuminate the target point (in the case of a so called non-cooperative target) or points or a cooperative retro-reflecting target or targets. The interferometer provides some means of splitting light from a light source into a reference and measurement beam. The measurement beam is directed towards the target point (or points), which reflect some of the incident light back to the interferometer. The reference beam is reflected by a reference mirror within the interferometer so that the returning reference beams and measurement beams are combined at a detector or receiver.
FSI uses a tuneable laser as a light source. The frequency of the light from the tuneable laser is swept through a range of frequencies. When this is done, a sinusoidal signal is received at the detector. The frequency of this signal is proportional to the distance to the target, and hence measuring the signal frequency allows the distance to the target to be measured. This is shown in FIG. 2 where the reflected frequencies are represented against the time of arrival to the receiver. The observed frequency difference (beat frequency), ΔF is proportional to the round-trip time of the measurement beam, τ, which is related to the distance, D, to the target through the speed of light, c.
  D  =      c    ⁢          τ      2      
Taking advantage of the continuous sweep, the time delay caused by the different distance creates a beat frequency. The frequency of this beat is directly proportional to the distance to the target if the sweep is linear (or if it is linearized through another reference) and since frequency processing though the FFT is easier and more reliable than a time delay measurement this method is particularly useful for precise measurements.
Different alternatives of this design have been suggested, ranging from simple systems that rely on frequency only to more complex systems that add phase measurement (which improves precision but the system is less flexible due to additional references required and problems arise if the signal is lost at any point).
In FSI, the optical frequency of the laser during a measurement can be described with the following equation:f(t)=2π(αt+f0)
Where f(t) is the optical frequency of the laser light, a is the rate of change of laser frequency,
      -          T      2        <  t  <      T    2  is the time (where T is the total measurement time) and f0 is the laser frequency at t=0. With this sweep the intensity of the field after the interferometric detection, if we eliminate the DC and high frequency components, matches the following expression:
      I    ⁡          (              t        ,        τ            )        =      A    ·          cos      ⁡              [                  2          ⁢                      π            ⁡                          (                                                ατ                  ⁢                                                                          ⁢                  t                                +                                                      f                    0                                    ⁢                  τ                                -                                                      ατ                    2                                    2                                            )                                      ]            
τ is the time delay between the reference mirror and the target, and at is the measured beat signal frequency ΔF in FIG. 2. The τ2 term is usually negligible and is therefore discarded. This expression can be easily evaluated through a frequency Fourier analysis (for example by fast Fourier transform, FFT) and if τ is constant this will give a clear peak at the frequency, ΔF, that corresponds to the distance to the target. In non-ideal situations, a problem appears when the target is moving, either intentionally or due to vibration, or if the optical path is changing due to e.g. air motion, and thus τ has a dependence of t. As f0 is large in comparison to the other terms in the argument of the cosine, even small variations of T during a measurement can cause a large disturbance to the signal. This Doppler shift greatly increases the distance measurement uncertainty, both through increasing the variance of measurements when the target movement is random between measurements (e.g. when caused by vibration), and by the presence of systematic errors present when the target motion is at a constant rate.
The use of two different sweeps (from two different optical sources) has been applied to solve this problem. This is known as Dual-sweep FSI. For example the system described in U.S. Pat. No. 8,687,173 uses two tuneable laser operated at two different tune rates and tuned in opposite directions (one up and one down in frequency) to produce a single signal on a single photodetector with two frequency components; one from each laser. By separating the two signals in frequency, they can be independently processed to determine a single distance measure that is largely free of Doppler induced error.
An alternative solution was proposed by Schneider et al (2000) in which two lasers operated at the same tuning rate, but in opposite directions to produce two signals. The lasers need to be separated (in frequency, polarization or other technique) so they can be independently detected by two different receivers where we will have the following signals:
                    I        1            ⁡              (                  t          ,          τ                )              =          A      ·              cos        ⁡                  [                      2            ⁢                          π              ⁡                              (                                                                            α                      1                                        ⁢                    τ                    ⁢                                                                                  ⁢                    t                                    +                                                            f                                              0                        ,                        1                                                              ⁢                    τ                                    -                                                                                    α                        1                                            ⁢                                              τ                        2                                                              2                                                  )                                              ]                                        I        2            ⁡              (                  t          ,          τ                )              =          A      ·              cos        ⁡                  [                      2            ⁢                          π              ⁡                              (                                                                            α                      2                                        ⁢                    τ                    ⁢                                                                                  ⁢                    t                                    +                                                            f                                              0                        ,                        2                                                              ⁢                    τ                                    -                                                                                    α                        2                                            ⁢                                              τ                        2                                                              2                                                  )                                              ]                    
Multiplying I1(t,τ) and I2(t,τ), we obtain
                    I        1            ⁡              (                  t          ,          τ                )              ·                  I        2            ⁡              (                  t          ,          τ                )              =            1      2        ⁢                  A        1            ·              A        2            ·              {                              cos            ⁡                          [                              2                ⁢                                  π                  ⁡                                      (                                                                                            (                                                                                    α                              1                                                        -                                                          α                              2                                                                                )                                                ⁢                        τ                        ⁢                                                                                                  ⁢                        t                                            +                                                                        (                                                                                    f                                                              0                                ,                                1                                                                                      -                                                          f                                                              0                                ,                                2                                                                                                              )                                                ⁢                        τ                                                              )                                                              ]                                +                      cos            ⁡                          [                              2                ⁢                                  π                  ⁡                                      (                                                                                            (                                                                                    α                              1                                                        -                                                          α                              2                                                                                )                                                ⁢                        τ                        ⁢                                                                                                  ⁢                        t                                            +                                                                        (                                                                                    f                                                              0                                ,                                1                                                                                      -                                                          f                                                              0                                ,                                2                                                                                                              )                                                ⁢                        τ                                                              )                                                              ]                                      }            
Making the lasers sweep their frequencies at the same speed, but in opposite directions (in which case, α1=−α2, and f0,1≈f0,2) the above expression becomes
                    I        1            ⁡              (                  t          ,          τ                )              ·                  I        2            ⁡              (                  t          ,          τ                )              =            1      2        ⁢                  A        1            ·              A        2            ·              {                              cos            ⁡                          (                              4                ⁢                                  πα                  1                                ⁢                τ                ⁢                                                                  ⁢                t                            )                                +                      cos            ⁡                          (                              4                ⁢                π                ⁢                                                                  ⁢                                  f                                      0                    ,                    1                                                  ⁢                τ                            )                                      }            
The first term is a cosine with a frequency proportional to the distance to be measured, but which does not suffer from a large disturbance when τ varies during a measurement. The second term is a low frequency signal, and does not interfere with our analysis.
Alternatively, if α1=−α2, and f0,1≠f0,2 expressing the average of f0,1 and f0,2 as fp, and multiplying I1(t,τ) and I2(t,τ), we obtain
                    I        1            ⁡              (                  t          ,          τ                )              ·                  I        2            ⁡              (                  t          ,          τ                )              =            1      2        ⁢                  A        1            ·              A        2            ·              {                              cos            ⁡                          (                                                4                  ⁢                                      πα                    1                                    ⁢                  τ                  ⁢                                                                          ⁢                  t                                +                                                      (                                                                  f                                                  0                          ,                          1                                                                    -                                              f                                                  0                          ,                          2                                                                                      )                                    ⁢                  τ                                            )                                +                      cos            ⁡                          (                              4                ⁢                π                ⁢                                                                  ⁢                                  f                  p                                ⁢                τ                            )                                      }            
Again, the first term is a cosine with a frequency proportional to the distance to be measured, but which does not suffer from a large disturbance when T varies during a measurement. The second term is a low frequency signal that conveys information about the relative motion (either mechanical motion or optical path length variation) between the sensor and target.
In the equations above, t represents time and it is assumed that α1 and α2 vary linearly with time. If α1 and/or α2 do not vary linearly with time, t, then parameter t could be replaced with another parameter, i, with which α1 and α2 do vary linearly.
This scheme can be realised using two separate tuneable lasers that are operated in a synchronised way to tune at exactly the same rate, but in opposite directions.
The tuneable lasers required in dual-sweep FSI systems are often the most expensive component in this type of system (particularly if high precision is required which requires large mode-hop-free tuning range), and synchronising their frequency sweeps with sufficient accuracy can be difficult. The distance resolution/accuracy that can be achieved is related directly to the frequency range over which the laser can be mode-hop-free tuned. Generally, the larger the tuning range of the laser the greater the cost.
There have been attempts to improve on accuracy of dual-sweep FSI systems that, for example, include different combinations of lasers and synchronisation methods.
However, despite improvements, the approach remains very expensive and complex to implement and maintain.
FSI uses heterodyne detection to generate a sinusoidal signal by beating the measurement beam with the reference beam as illustrated in FIG. 11, which shows a circulator being used to take a tuned laser output. A fraction of the light passed through the circulator from the laser is reflected back from the end face of the fibre forming the reference signal. The majority of the light projects into space where it is reflected by one or more targets. The reflected light returns to the fibre end and couples back into the fibre and is directed by the circulator along with the reference beam to a photodetector where the beams interfere and produce a signal. The reference beam thus performs the role of local oscillator (LO). It is generally know that the signal amplitude is proportional to the product of the LO and measurement beams amplitudes. So increasing the LO or measurement beam amplitude results in higher signal levels. But, for industrial applications, the measurement beam must be kept eye-safe to prevent injury to the user. This limits the amount of signal gain that can be obtained by increasing the measurement beam amplitude. Improved signal gain can therefore be best achieved by control of the reference beam amplitude.
A convenient way of generating the LO beam is by back reflection from the end of an optical fibre that is used to transmit the laser light to the point on the measurement. This conveniently places the measurement datum at the physical end of the fibre (as in FIG. 8). A second advantage of this approach is that disturbances to the measurement and reference beams as they propagate down the fibre due to stresses in the fibre (temperature, physical strain etc) are common-mode and do not contribute to the signal detected at the detector.
However, taking the LO signal from the fibre end in this way limits the amount of signal gain that can be achieved. An un-modified fibre will reflect approximately 4% of the incident light resulting in a weak LO signal. The reflectance can be increased by coating the end of the fibre. But increasing the reflectance to increase the LO signal degrades the measurement signal as it is coupled back into the fibre on return from the target(s). The optimum reflectance is 33%.
An alternative way of deriving the LO reference is to use a splitter with a split ratio R:T as illustrated in FIG. 12. The splitter sends R % of the light into the LO beam and T % into the measurement beam. A circulator is again used to direct the measurement beam out into space and return the measurement beam down the return fibre. The LO and measurement beams are then combined by a 50:50 coupler to produce two signals that can be detected using a balanced detector. This setup has the advantages that the gain can be controlled by setting the R:T ratio and laser power appropriately to result in the desired signal gain whilst maintaining eye-safe power levels in the measurement beam.
The draw-back of this approach is that the LO and measurement beams no longer take a common path through the optical fibres, so any disturbance to the fibres due to, for example, temperature change or other stresses will result in drift in the distance measurements. In other words, the measurement datum is not well defined.
The challenge is therefore to produce a system that is cost effective, can operate to measure multiple targets simultaneously (for coordinate metrology applications), has sufficient optical gain to provide robust signals and provides a reliable, drift free measurement datum.